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ZanzabumX [31]
2 years ago
8

Convert 0.181818 … to a fraction by writing the repeating decimal as an infinite geometric series. Show all of your work (please

)
Mathematics
1 answer:
allsm [11]2 years ago
3 0

0.181818… = 18 (0.010101…)

… = 18 (0.01 + 0.0001 + 0.000001 + …)

… = 18 (1/100 + 1/100² + 1/100³ + …)

… = 18 (1 + 1/100 + 1/100² + 1/100³ + …) - 18

Then you have

0.181818\ldots = \displaystyle18\sum_{k=0}^\infty\frac1{100^k} - 18 = \frac{18}{1-\frac1{100}} - 18 = \boxed{\frac2{11}}

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Answer:

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Let x represent Jim's hourly pay.

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